How to export white/shadow catcher with filmic?
the background with shadows divided by a clean background with no shadows does not generate white.

If you are dividing any value by itself the result will be one: $\frac{X}{X} = 1$
The standard sRGB transform will display white when the scene value reaches 1
But &quot;white&quot; doesn't live there any more if you are using filmic blender's color transforms.
&quot;White&quot; is not equal to 1, 1, 1,
White is somewhere around 16.29174024 in scene referred values (and operations before the color management, like nodes in the compositor, are done with scene referred data. The color transforms to create display referred images out of that data are done at the very end of the pipeline).
Filmic blender uses a much wider dynamic range, Using the filmic blender transforms you need a much higher value to reach &quot;white&quot;, most likely you would need to scale the result of that division by 16.29174024 with a multiply node to fall within the parameters that work with filmic blender.

To understand what filmic blender does and how it maps the scene's values to the displayed image please read the following link: Render with a wider dynamic range in cycles to produce photorealistic looking images
and https://github.com/sobotka/filmic-blender